Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems

By Dinh Tuan Pham. 2001

477 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Atmospheric Science, Oceanography

View Paper: https://www.semanticscholar.org/paper/15c8eb87816b5da4c4fe68ed791cd5489c61f959

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Citations in the corpus

A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation (2015, methodology): “A popular approach, initiated by Anderson and Anderson (1999) and Pham (2001), is the representation of the forecast ensemble as aGaussianmixture, allowing a better consideration of nonlinear features contained in the ensemble (e.g., Hoteit et al. 2008; Stordal et al. 2011; Hoteit et al. 2012; Frei…”
Ensemble Kalman filtering (2005, unknown): “Second-order-exact sampling of random numbers has been discussed by Pham (2001).”
The potential of the ensemble Kalman filter for NWP—a comparison with 4D‐Var (2003, methodology): “Such methods have been demonstrated successfully for simple low order models (Pham 2001; Anderson 2003).”
The Ensemble Kalman Filter: theoretical formulation and practical implementation (2003, methodology): “…ﬁlters based on either kernel approximation or particle interpretations have been proposed by Miller et al. (1999), Anderson and Anderson (1999), Pham (2001), Miller and Ehret (2002), and van Leeuwen (2003), although more research is needed before these can claimed to be practical for realistic…”
Obstacles to High-Dimensional Particle Filtering (2008, background): “Furrer and Bengtsson (2007) and Bickel and Levina (2008) examine the sample covariance structure for reasonably natural classes of covariance matrices and demonstrate the effectiveness of localizing the sample covariance matrix.”
Particle Filtering in Geophysical Systems (2009, methodology): “…5 n 1 2 2g (1 2 jc 2 c i j2) for jc 2 c i j, 1, (20) and zero otherwise, where n is the dimension of c and g is the volume of a unit sphere in Rn. Pham (2001) proposes to sample new particles from a Gaussian density centered around particles with multiple identical copies, found from…”
Ensemble Data Assimilation without Perturbed Observations (2002, methodology): “Pham (2001) introduced a method for perturbing observations that guarantees that the background-observation-error covariance terms in Eq.”
Sequential Data Assimilation Techniques in Oceanography (2003, methodology): “Some of them have been compared experimentally to simulated test cases (Cañizares, 1999; Verlaan, 1998; Pham, 2000; Verlaan & Heemink, 1999) focusing on computer time, robustness of the algorithms to nonlinearities (Verlaan & Heemink, 1999), and robustness to systematic errors and to incorrect speci”
A comparison of error subspace Kalman filters (2005, methodology): “In particular, no techniques to stabilize the filters, e.g. by localization of the analysis (see, for example, Houtekamer and Mitchell, 2001) or by forgetting factors (see, for example, Pham, 2001; Whitaker and Hamill, 2002), are used.”
A Moment Matching Ensemble Filter for Nonlinear Non-Gaussian Data Assimilation (2011, background): “Some systematic sampling schemes are often used to make sure that the perturbations have zero mean, covariance R, and zero correlation with the forecast ensemble (Pham 2001).”
A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography (2008, methodology): “The initial particles x1|10 were then randomly sampled using the second-order exact drawing scheme (Pham 2001).”
A Method for Assimilation of Lagrangian Data (2003, methodology): “The method is compared to an alternative indirect approach, where the flow velocity, estimated from two (or more) consecutive drifter observations, is assimilated directly into the model.”
Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF (2015, methodology): “This same ensemble framework is also used by other ensemble-based Kalman filters, including the singular evolutive interpolated Kalman (SEIK) filter (Pham 2001), the ensemble transform Kalman filter (ETKF) (Bishop et al. 2001), the ensemble adjustment Kalman filter (EAKF) (Anderson 2001), the…”
Snow water equivalent prediction using Bayesian data assimilation methods (2011, background): “Resampling is implemented only when entropy difference (Ept) is greater than a prescribed threshold, Epthresh (Pham 2001).”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, methodology): “Thus, we write the symmetric square root solution Equation (54) as Xa =XfZ ffiffiffiffi Λ p ZTΦT, ð55Þ where Φ is a mean-preserving random orthogonal matrix, which can be computed using the algorithms from Pham (2001) or Sakov and Oke (2008a).”
Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters (2008, methodology): “In the singular evolutive extended Kalman filter (SEEK) and singular evolutive interpolated Kalman filter (SEIK; Pham et al. 1998; Pham 2001), the analyzed error covariance is calculated via updating of the eigenvalues of the covariance matrix with subsequent redrawing of the ensemble anomalies.”
Ensemble size, balance, and model-error representation in an ensemble Kalman filter (2002, methodology): “Pham (2001) has presented a method of perturbing observations subject to additional constraints, while Anderson (2001) and Whitaker and Hamill (2002) have presented EnKF algorithms that do not require the observations to be perturbed at all.”